Question

Suppose for some unexplained reason you were skateboarding (or skiing, if that�s your taste) and wanted to use a spring to launch you off a frictionless ramp. Assuming you have a mass of 70 kg, if the spring has a spring constant k 5 625 N/m and is compressed 5 m,

1. If the ramp has a 60� slope and goes up 8 m high, will you make it off the ramp? If so, what will your velocity be as you are leaving the ramp?

2. How high will you go?

3. How fast will you be going when you enter the ramp? (Ignore friction.)

4. Suppose the ramp were not frictionless, and you only make it up 4 m high. Find the heat (in joules) lost
due to friction.

5. Given your answer to question 4, find the frictional force and the coefficient of kinetic friction.

Answer 1

here,

mass , m = 70 kg

spring constant , k = 5625 N/m

x = 5 m

(a)

theta = 60 degree

height of ramp , h = 8 m

to make it off the ramp

0.5 * k*x^2 >= m*g*h

0.5 * 5625*5^2 >= 70 * 9.8* 8

70312.5 >= 5488

therefore , it will take off the ramp

let its velocity at take off be v

0.5 * k*x^2 = m*g*h + 0.5 * m*v^2

0.5 * 5625 *5^2 = 70 *9.8*8 + 0.5 * m*v^2

v = 43.04 m/s

the speed is 43.04 m/s

(b)

let the height be h

h = v^2sin^2(theta) /( 2g)

h = 43.04^2 * 0.75 /( 9.8*2)

h = 70.88 m

the height reached is 70.88 + 8 m

the height reached is 78.88 m

(c)

let the speed when i enter the ramp be v0

0.5 * m*v0^2 = 0.5 * k*x^2

0.5 * 70 * v0^2 = 0.5 * 5625*5^2

v0 = 44.82 m/s

the initial speed is 44.82 m/s

(d)

let the froictional force be ff

0.5 * k*x^2= m*g*4 + ff

0.5 * 5625 * 5^2 = 70 * 8 * 9.8 + ff

ff = 67568.5 J

the heat energy lost is 67568.5 J